Radix

In the world of computer science and programming, understanding the concept of radix is fundamental to working with digital numeral systems. Radix, also known as the base number, plays a crucial role in determining the number of unique digits used to represent numbers in a positional numeral system. In this article, we will delve into the significance of radix and explore code examples in popular programming languages such as C#, JavaScript, Python, and PHP.
What is Radix?
Radix refers to the number of unique digits, including zero, used to represent numbers in a positional numeral system. It determines the base of the system and governs how numbers are expressed. For instance, in the decimal or denary system, which is the most commonly used system today, the radix is ten. This means that the system utilizes ten digits, from 0 to 9, to represent numbers. In binary, the radix is two, as it only uses two digits, 0 and 1.

The Importance of Radix in Digital Numeral Systems

Radix plays a crucial role in digital numeral systems as it determines the range of possible digits and allows us to express numbers efficiently. By using a positional system, where the value of a digit depends on its position within a number, we can represent larger numbers using a limited set of digits. The radix specifies the number of distinct symbols available for use, enabling us to construct numbers by combining these symbols in different positions.

In the above code examples, we convert a decimal number (42) to its binary representation using the respective language’s built-in functions. The radix (2) is specified as the second argument in the conversion functions. We then convert the binary representation back to decimal using the radix to verify the accuracy of the conversion.

Links

Code Examples

C#
int number = 42;
string binary = Convert.ToString(number, 2);
Console.WriteLine(binary); // Output: 101010

int decimalValue = Convert.ToInt32(binary, 2);
Console.WriteLine(decimalValue); // Output: 42

JavaScript
let number = 42;
let binary = number.toString(2);
console.log(binary); // Output: 101010

let decimalValue = parseInt(binary, 2);
console.log(decimalValue); // Output: 42

Python
number = 42
binary = bin(number)
print(binary) # Output: 0b101010

decimalValue = int(binary, 2)
print(decimalValue) # Output: 42

PHP
$number = 42;
$binary = decbin($number);
echo $binary; // Output: 101010

$decimalValue = bindec($binary);
echo $decimalValue; // Output: 42

Conclusion